Journal of Mathematical Biology

Approximate Bayesian computation sequential Monte Carlo (ABC-SMC) propagates its particles with a perturbation kernel, and with the standard Normal kernel it degrades sharply as the parameter dimension grows, a failure usually attributed to dimension itself. We show instead that it is governed by the quality of the summary statistics, with dimension entering only through a separate and milder mechanism, and that the two must act together for the Normal kernel to break. The first ingredient is covariance overinflation: the kernel covariance, estimated from the particle cloud, overshoots the true posterior covariance by a factor set by information loss in the summary statistics. We derive this overscaling factor in closed form for a Gaussian model with sufficient statistics and show that it stays modest at any dimension, shrinking toward its baseline value as the tolerance tightens; the extreme values seen in practice (of order 103) are a signature of insufficient summaries, not of dimension. The second ingredient is perturbation overconcentration: the normalised Normal step size concentrates around one as the dimension grows, so every proposal overshoots by the same factor. Either ingredient alone is harmless; only their combination breaks the Normal kernel. A Cauchy kernel (multivariate t with one degree of freedom) removes the concentration, keeping a positive acceptance rate under arbitrary overscaling at a bounded worst-case cost of 1.87x in expected squared jump distance. In a Metropolis-Hastings framework we derive closed-form acceptance rates for both kernels that illustrate the advantage of the Cauchy kernel in this limit. A series of full ABC-SMC computational experiments on five problems at d = 12, including a hierarchical gene-expression model, show the Cauchy reducing the sliced Wasserstein distance to the reference posterior by factors of up to 50 with the same simulation budget. Since the summary statistics are commonly insufficient for the models that require ABC, overinflation is structural and the Cauchy perturbation kernel is the right default for problems in higher dimensions.

The osteocyte network in bone is believed to play an important role for how bone tissues sense and respond to mechanical stimulation. Yet, bone adaptation to mechanical loads is often conceptualised as a simple response to mechanical stimuli, such as Wolffs law, which is based on mechanical variables only and takes no account of the cellular basis of mechanosensation. Wolffs law presumes the existence of a reference mechanical stimulus, the mechanical setpoint, above which bone is consolidated, and under which bone is removed. In this paper, we develop a theory of bone tissue sensing and adaptation based on osteocytes to provide new understanding of the role played by osteocyte signals in mechanical adaptation. In this theory, the mechanical setpoint of Frosts mechanostat is explicitly embodied as osteocyte properties involved in mechanotransduction. The mechanical setpoint is allowed to adapt due to the replacement of osteocytes during remodelling, making the setpoint space and time dependent. We propose a mathematical model to implement this new theory of bone adapation and present numerical simulations of this model to explore how mechanobiological response curves (effective Wolffs laws) are modulated by setpoint adaptation during remodelling. By accounting for varying osteocyte populations within bone tissue, we explore bone adaptation under osteocyte disruptions, which is particularly relevant to age-related bone loss. Our model suggests that biological disruptions of remodelling balance cannot always be compensated by mechanical feedback, and that setpoint adaptation during remodelling may have significant observable consequences, such as hysteresis in bone response signatures that resemble lazy zones.

Diffuse gliomas are deadly because the individual tumor cells invade - they travel far from the imageable mass, so it is impossible to remove the tumor completely. On the cellular level, glioma cells seem to be in either a "go" state (in which they do not divide) or a "grow" state (in which they do not migrate). We investigate what this tiny choice has to say about the large-scale speed of the invasion front and whether the implication is sufficiently strong to rule out the classical description of the Fisher-Kolmogorov-Petrovsky-Piskunov (Fisher-KPP) type, in which a single phenotype migrates and proliferates. We derive a two-phenotype reaction-diffusion model with density-dependent switching, and we prove the cooperative (quasi-monotone) structure and the associated comparison principle and study travelling-wave solutions of the model. A leading-edge linearization gives minimal front speed as minimizer of an explicit dispersion relation, and direct simulation verifies the predicted speed. In the experimentally relevant fast switching limit, we find a closed-form expression for the speed, that is, we obtain an effective Fisher-KPP equation with rescaled diffusivity and growth rate, with the fractions of the phenotypes. The "go-or-grow" (GoG) front can move at a maximum speed of half the Fisher speed for the same single-cell motility $D$ and proliferation rate $r$, which occurs only when the cells divide their time equally between the two phenotypes. This bound is directly testable: measurement of the front speed, plus independent determination of $D$ and $r$, discriminates the two hypotheses, and in the GoG case, yields recovery of the phenotype balance. We then extend the result to anisotropic (DTI-informed) invasion along white-matter tracts and discuss implications for understanding clinical measurements of growth rate.

Environmental variability can strongly alter coexistence among competing species and their extinction risk, particularly when population dynamics are shaped by behavioral interactions, such as fear. In this work, we develop a novel stochastic differential equation competition model that incorporates both non-consumptive fear effects and environmental variability to investigate how behavioral interactions influence species coexistence under random fluctuations. Our result reveals that environmental stochasticity can drive species to extinction even when the corresponding deterministic system admits coexistence. In particular, under an explicit stability condition on the fear and competition parameters and sufficiently strong averaged noise intensities, we prove that both competing species become extinct exponentially almost surely. Conversely, we derive a stochastic persistence criterion in terms of fear, competition, and noise-induced suppression parameters for the fearful species. We further demonstrate that environmental noise may reverse classical competition-exclusion outcomes, leading to qualitatively different long-term dynamics from those predicted deterministically. These results provide rigorous thresholds separating stochastic extinction from persistence and highlight the critical role of environmental variability in fear-mediated competitive ecosystems. From an applied perspective, these results provide insight into how behavioral interactions and environmental variability influence species survival, with potential applications in ecological management and conservation.

AO_SCPLOWBSTRACTC_SCPLOWCell fate decisions are driven by gene regulatory networks (GRNs). While the mutually inhibitory toggle switch effectively models binary fate decisions, fully connected inhibitory networks with more than two nodes fail to capture multi-fate decisions due to the low prevalence of "single high states", where only a single master regulator is highly expressed. The goal of this study is to find network structures that support all single high states. We find that the only network that attains the highest possible prevalence of all single high states within the set of monotone Boolean (MB) models is completely disconnected. Since biological networks typically require connectivity, we investigate network structures that support equipotency, where all single high states have equal prevalence within MB models. Finally, we characterize the networks that support multistability between all single high states, finding that it is possible only in networks in which each node either has self-activations or is inhibited by every other network node. Our findings provide a theoretical framework for understanding the network design principles that can support simultaneous differentiation into multiple distinct cell types.

AO_SCPLOWBSTRACTC_SCPLOWO_LICommunity assembly graphs (CAGs) summarize which species combinations can coexist and how single-species invasions drive transitions between them, encoding the pathways, alternative endpoints, and cycles that make up a communitys assembly history. Constructing CAGs from dynamical models requires methods that are both computationally tractable and faithful to the underlying ecological dynamics. However, existing methods rely on restrictive assumptions, such as global stability, that exclude alternative stable states and non-equilibrium dynamics known to occur in empirical systems. C_LIO_LIWe develop a computational pipeline that constructs CAGs from any generalized Lotka-Volterra model. Building on the invasion graph framework and its connection to permanence, the pipeline verifies that community dynamics are bounded, identifies which subsets of species coexist in the sense of permanence, determines which single-species invasions are dynamically realized, and assigns each community a topographic height equal to the length of the longest assembly path leading to it. We also provide a numerical algorithm to simulate the dynamics of community assembly. C_LIO_LIWe prove several general properties of the resulting graphs, including that a successful invader is never subsequently excluded and that, in the absence of assembly cycles, permanent communities can be reassembled by introducing their species one at a time in the right order. We prove that the CAG faithfully reproduces the compositional shifts seen in the numerically simulated dynamics of assembly. Applying the pipeline to three empirically based models (a New Zealand grassland, a European pasture, and a Puerto Rican ant community), we show how competition strength and mutualistic feedbacks reshape the assembly landscape and how intransitive competition generates assembly cycles. C_LIO_LIOur approach accommodates alternative stable states and non-equilibrium dynamics without requiring global stability, and it turns the long-standing landscape metaphor into a quantitative, mechanistically grounded object by resolving what "height" means. More broadly, it makes the topography of the assembly pathways measurable, providing a way to compare the historical contingency and predictability of the assembly in ecological systems. C_LI

Biomolecular condensates are widespread cellular self-assembled structures with essential functions. There are suggestions of condensates formed by different proteins being near criticality. However, systematic investigation of the criticality of condensates is absent, and critical exponents defining their universality class have not been found. Here, using long-time simulations, we show that condensates exhibit typical critical phenomena, including scale-free spatiotemporal correlations, critical slowing down, divergence of correlation length and dynamic scaling. From these scaling behaviors, a set of critical exponents is determined. Based on dynamic critical exponent, diverse condensates can be divided into two distinct universality classes, arising from differences in their molecular components and interaction types.

We develop a mathematical model of Rift Valley Fever integrating mosquito vectors, ruminants, and humans, based on an SEIR-type structure with vertical transmission in vectors. Local data from the Sudanian and especially the Sahelian zones are used to capture the impact of climatic variations on mosquito population dynamics. The mathematical analysis establishes the models positivity, determines the basic reproduction number R0, and demonstrates the local and global stability of the disease-free equilibrium. Sensitivity analysis (PRCC) highlights the most influential parameters, while the stochastic approach using a continuous-time Markov chain confirms the major role of seasonal rainfall. Numerical simulations reveal a peak in animal and human infections around the 9th month, correlating with periods of heavy rainfall. This model provides a relevant tool for surveillance and prevention within a "One Health" approach in Chad.

Cell shape and mechanics are intricately connected and tightly regulated by mechanochemical events including biochemical signaling, cytoskeletal remodeling, and plasma membrane mechanics. While experimental advances in microscopy have shed light on the intricate coordination involved in cell shape change in response to different cues, the ability to conduct three-dimensional simulations in realistic geometries remains an open computational challenge. In this work, we develop a finite-element framework that incorporates advection-diffusion-reaction equations coupled with equations governing the kinematics of a deformable interface representing the cell membrane. We applied this framework to three distinct coupled mechanochemical systems, each governed by geometric partial differential equations, resulting in large deformations of the interface. In all three examples, our simulations revealed the emergence of feedback between cellular signaling, cytoskeletal organization, and cell shape. In our first two sets of simulations, we observed that cell migration and neutrophil protrusion were regulated by membrane tension-mediated feedback. In our final application, we predicted shape changes of a dendritic spine starting from a realistic geometry, and found that the complex shape of the spine gives rise to localized regimes of actin cytoskeleton remodeling not previously observed with idealized geometries. Thus, our finite-element framework allows us to generate new mechanistic insights for biophysical problems.

Cetaceans reduce the net cost of sustained swimming through intermittent locomotion, alternating active fluking with unpowered gliding. The energy balance of this strategy is central to understanding survival rates, population sustainability, and the effects of anthropogenic and environmental pressures. While active-phase energetics have been characterized extensively, the glide phase remains largely unexplored. Here we derive the optimal glide duration (Topt) and the maximum glide duration beyond which energy savings vanish (Tzero) for three odontocetes spanning a 20-fold range in body mass, using high-fidelity CAD models and wall-modeled large eddy simulations. We show analytically that speed retention at Topt and mass-specific peak energy savings are both fully determined by the active-to-passive drag ratio, propulsive efficiency, and swimming speed, independently of body morphometry and drag coefficient, and are therefore invariant across species at any given speed. These passive-phase optima extend the known size-independent active-phase invariants to the glide phase, towards a scale-independent energetic framework for burst-and-glide locomotion in small cetaceans.

In this paper, we propose a new model to estimate the impact of an intervention on human hosts of a vector-borne infection, such as dengue, which occurs in yearly outbreaks of different magnitudes. The model applies to these outbreaks and, in fact, is independent of their intensity, that is, it does not require the steady-state assumption. The model takes as input the officially reported age-dependent number of cases of a vector-borne infection. It is deterministic and does not account for stochasticity. Our objective is to estimate the impact of the intervention (the efficacy), and we rely on the observed fact that the age distribution of the proportion of cases of the infections transmitted by the same vector is independent of both the intensity of transmission and the geographic area studied, at least for Brazilian regions. This finding is highlighted in the main text and forms the basis of our calculations. A hypothetical intervention is simulated using a dengue vaccine, which allows the determination of the optimal strategy for a vaccination campaign.

The relationship between genotypic and phenotypic variation is determined by the complex interaction of genetic and environmental factors. While statistical methods capable of detecting such interactions exist, an axiomatic mathematical framework that seamlessly describes the combined effects of genetic modifications and environmental exposures on a common scale is lacking. In this report, buffering concepts are used to construct a measurement system that enables the geometric representation of both gene-by-gene and gene-by-environment interactions on the extended complex plane (i.e., as projections on the Riemann sphere). In this manner, any such interaction, or combination thereof, can be precisely defined and quantified as the deviation from the neutral value calculated through the applicable complex transformation. When thus conceptualized, the framework's parameterization defines the "state space" of a given measurable phenotype along both the real and imaginary dimensions, thus establishing an unambiguous and broadly applicable method for determining the phenotypic value expected upon combinatorial changes in genetic and/or environmental variables. Remarkably, by applying these methods, it is possible to quantify the effects of any gene-by-environment interaction using the equation, AGxE=Im([z]obs*zexp)/2, where zobs and zexp are complex numbers representing the observed and expected phenotypes of a given genotype expressed in terms of the buffering parameters, and b.

Mechanistic ordinary differential equation models are widely used in systems biology to represent biochemical networks, population dynamics, cell-state transitions, and other biological processes; however, their predictive value depends critically on accurate parameter estimation from noisy and often sparse experimental data. In this tutorial, we present the Weak-form Estimation of Nonlinear Dynamics (WENDy) method as a forward-solver-free approach that reformulates parameter estimation as a covariance-corrected weak-form regression problem by integrating the model equations against compactly supported test functions. We present the background on the methodology through the lens of the familiar logistic equation, and we demonstrate applications of the method on real experimental data through two systems biology examples: a glycolytic oscillator with relatively dense time-course data and a sparse epithelial-mesenchymal cellstate transition model with multiple experimental replicates. Ultimately, using WENDy, we estimate interpretable biological parameters with uncertainty for systems with noisy and sometimes sparse available experimental data.

Microbes exhibit complex dynamic behavior as the result of a large number of biochemical processes, spatial and temporal interactions, environmental variations, and evolutionary pressure. Although significant progress has been achieved in understanding microbial ecological dynamics, multiple open questions remain, including the microscopic mechanisms of growth and the roles of nutrients and stochasticity. In this work, we present a minimal theoretical approach to clarify the link between consumption of resources by microbes and their growth. A stochastic model that accounts for a single microbial species consuming a single type of resource while growing via cell division is studied analytically and via Monte Carlo computer simulations. We identify three distinct dynamical regimes of microbial growth determined by the relative magnitudes of resource uptake and division rates and initial conditions. We also show that stochasticity influences the dynamic behavior when the amounts of microbes or resources are low. The model recovers Monod growth kinetics and provides a mechanistic interpretation of the Monod constant and maximal growth rate. The theoretical framework presented captures a wide spectrum of dynamic behaviors in microbial systems, providing a clearer microscopic picture to explain their underlying complex mechanisms.

The mosquito Aedes albopictus is a competent vector for the transmission of several arboviruses and is currently spreading across many continents. Since conventional control methods, like insecticides, often lead to environmental problems and the emergence of resistance, scientists developed alternative mosquito control strategies. One of the most used is the Sterile Insect Technique (SIT), which involves the mass release of males sterilized through irradiation. The Toxic Male Technique (TMT) is instead based on the release of genetically modified males expressing toxic proteins that kill females when they mate. Control strategies are often intended as methods to eradicate mosquito populations, yet a less ambitious and more cost-effective task is to reduce them such that the probability of transmission of viruses to humans becomes negligible. To compare the efficacy of these control strategies, we develop a mathematical model with two communicating compartments: a mosquito population and epidemiological model coupled with a human epidemiological model. As a proof-of-concept, we test the model using meteorological and entomological data for the Emilia-Romagna region. Our results indicate that the TMT strategy is more effective in lowering the probability of transmission and provides indication for the deployment of control strategies.

Compartmental models of infectious disease transmission make assumptions about human behaviors. Specifically, they parameterize interactions across population groups, assumed to have distinct epidemiologically-relevant behavioral patterns, primarily through contact matrices stratified by demographic variables such as age, gender, or socioeconomic status. Although such demographic characteristics are readily measurable, they may inadequately capture the social and psychological forces that govern protective behaviors. Drawing on 20 waves of a national survey conducted throughout the COVID-19 pandemic in the United States, we show that institutional trust - particularly trust in public health agencies, physicians, and hospitals - is a dominant predictor of protective behavior adoption. For mask wearing during periods of strongest pandemic activity, for example, institutional trust explains more behavioral variance across population groups than age, income, education, and partisan affiliation combined. In unadjusted analyses, the difference in protective behavior adoption between individuals with the highest and lowest trust in the CDC was four- to six-fold larger than the corresponding differences by age, income, or educational attainment, and exceeded the difference between Democratic and Republican respondents. This association was institutionally specific (e.g., the relationship attenuates for trust in banks), and behaviorally specific (e.g., trust in the CDC is associated with protective behaviors but not visiting a doctor). The latter suggests that trust modifies voluntary compliance with public health recommendations rather than access to or use of healthcare. We conclude that compartmental models of disease transmission would be substantially improved by incorporating institutional trust as a stratifying variable. We additionally offer a trust-integrated mathematical modeling framework and recommendations for the data infrastructure needed for its implementation.

Antifungal drug-resistant Candidozyma auris (C. auris) is a threat to human health worldwide. Combination antifungal drug therapy has emerged as a promising approach to combat drug-resistant C. auris because some drugs interact synergistically to increase fungal clearance when co-administered. Moreover, combination regimens that either rapidly act or completely kill C. auris could mitigate development of on-treatment resistance. However, traditional checkerboard methods to identify synergistic drug combinations only inspect fungal growth at a single timepoint. As a result, they cannot be used to estimate the rate of drug-action or to hypothesise on fungicidal or fungistatic drug-action. Mechanistic modelling would allow us to quantify time-dependent drug-action and infer killing or inhibitory action, but these models are usually fit to direct measurements of fungal growth whose collection is currently not scalable to many time-points and drug combinations. In this paper, we propose a Bayesian mechanistic modelling approach that could detect drug-synergy, estimate drug-action over time and investigate fungicidal or fungistatic drug-activity from optical density (OD600) data alone. OD600 is quicker and easier to collect than direct measurements of fungal growth and therefore more amenable to high-throughput susceptibility testing. By fitting our model to time-course OD600 data of a multi-drug-resistant C. auris isolate growing in mono- and combination drug regimens, we successfully inferred synergy between previously confirmed synergistic antifungal drugs (anidulafungin with manogepix or with 5-flucytosine) and linked our models inferred kinetic parameters to fungicidal and fungistatic action on C. auris growth, which matched drug-activity reported in literature where known. We validated that our model outperformed baseline logistic and Gompertz models using cross validation stratified by OD600 replicates. Our results represent the much-needed groundwork for identifying drug combinations for subsequent experimental testing for use in clinics based on their synergy, temporal drug-action and fungicidal or fungistatic activities inferred from OD600 data alone. Author SummaryThere is an urgent need to locate novel treatments to better treat antifungal drug-resistant Candidozyma auris infections. Combination therapy is a promising approach where two or more antifungal drugs are administered and interact synergistically to enhance fungal clearance. If these combinations are fast acting or eradicate fungi through killing, then they could also reduce the chance of resistance developing during treatment. The synergy of antifungal drug combinations is currently assessed by checkerboard methodologies that compare fungal growth under drug combinations to that under a single drug. However, checkerboard methodologies record only one time-point. Hence, they cannot evaluate drug combinations timeframe of action and follow-up studies are required to determine which combinations could optimally enhance killing. We developed a Bayesian mechanistic model that could detect synergy between drugs, estimate rates of drug-action and investigate killing and inhibition drug-action using only optical density (OD600) data of C. auris. OD600-based measurement of fungal growth is more amenable to large-scale drug testing than data typically used for mechanistic modelling, such as microscopy data. This work serves as a foundation for more targeted drug testing that identifies promising drug combinations based on their inferred drug-synergy and hypothesised killing (or inhibition) rates.

Under complex perturbation regimes, biodiversity dynamics show temporal variability in species and community abundance around long-term population trends. Many species indeed show long-term declines while other species increase, putting natural communities far from stationary regimes, while variability is often studied near equilibrium. We contribute to bridging this gap by investigating population and community variability during long-term trends caused by press perturbations in stochastic models of population dynamics. By estimating the deterministic changes in mean and variance during the transient regime, we show that population variability deviates from stationary expectations. Moreover, the deviation strongly depends on the sign of the population trends: increases generate excesses of variability while declines generate deficits. Scaling up to community variability, we propose a decomposition of community variability deviation, allowing to highlight that community variability in the transient regime depends on how the press perturbation is distributed within species relative abundances and growth rates. These results challenge the equilibrium assumption and open new perspectives for the study of the variability of ecological systems under multiple perturbation types.

The photosynthesis-transpiration-stomatal conductance (An-E-gs) model framework is widely used for estimating photosynthesis, transpiration, and stomatal conductance in plants. The model equations are solved by numerical iteration, and the converged model values are deemed the solution. However, there has been no general guarantee that the iterative procedure converges to a solution or that the procedure leads to convergence. Building on the recent proof of the existence of a unique set of solutions, we herewith propose a numerical algorithm that is guaranteed to converge to the solution for the An-E-gs model framework. We first analytically prove that the proposed algorithm necessarily converges to a solution. We then demonstrate the convergence across contrasting combinations of leaf temperature, relative humidity, light, atmospheric CO2, and wind speed. We further demonstrate rapid convergence with the algorithm: no more than ca. 10 iterations for approximately 10-3 mol CO2 m-2 s-1 precision in net photosynthesis and no more than ca. 20 iterations for 10-7 mol CO2 m-2 s-1 precision. By guaranteeing convergence to the solution, this algorithm eliminates concerns about nonconvergence in leaf gas-exchange calculations and is expected to serve as a robust foundation for a range of studies from leaf-level gas exchange to global-scale carbon and water cycle dynamics.

The aim of this paper is to model homeless accommodation settings to investigate how vaccination mitigates the outbreaks, highlighting the importance of vaccination in vulnerable settings. We estimate the daily per capita contact rate with wider community, the internal transmission rate, and the achieved vaccine coverage. We present stochastic simulation of the final size of disease outbreaks given choices of internal and external transmission. We conclude that vaccine that has effect in reducing transmission will mitigate the outbreak in homeless hostels but it will have better results when the household population has large vaccination coverage, which may lead to more cost from the health economic perspective.